Related papers: Action minimization and macroscopic interface moti…
Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Interfaces in tissues are ubiquitous, both between tissue and environment as well as between populations of different cell types. The propagation of an interface can be driven mechanically. % e.g. by a difference in the respective…
We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a…
Coarsening kinetics is usually described using a linear gradient approximation for the underlying interface migration (IM) rates, wherein the migration fluxes at the interfaces vary linearly with the driving force. Recent experimental…
We study a stochastic differential equation driven by a Poisson point process, which models continuous changes in a population's environment, as well as the stochastic fixation of beneficial mutations that might compensate for this change.…
What happens when the time evolution of a fluctuating interface is interrupted with resetting to a given initial configuration after random time intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};~\alpha > 0$? For an…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by…
Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with coupled material and geometrical…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
In mesoscopic scale microstructure evolution modeling, two primary numerical frameworks are used: Front-Capturing (FC) and Front-Tracking (FT) ones. FC models, like phase-field or level-set methods, indirectly define interfaces by tracking…
Wheelchairs and mobility devices have transformed our bodies into cybernic systems, enhancing our well-being by enabling individuals with reduced mobility to regain freedom. Notwithstanding, current interfaces of control primarily rely on…
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by applications in interface identification, where we assume…
We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition…
Despite the fundamental importance of solid-solid transformations in many technologies, the microscopic mechanisms remain poorly understood. Here, we explore the atomistic mechanisms at the migrating interface during solid-solid phase…
We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the…
In this paper we carry out a computational study of a novel microscopic follow-the-leader model for traffic flow on road networks. We assume that each driver has its own origin and destination, and wants to complete its journey in minimal…